ABSTRACT
2.1 Introduction
Many generalisations of the basic theory outlined in the previous chapter can be made. For example, we may allow the kernel to be a function of more than one sample, and consider so-called generalised U-statistics, which are the subject of Section 2.2 below. Generalising in another direction, we may relax the assumptions of independence and identity of distribution, as is done in Sections 2.3-2.5. We may also allow the form of the kernel to depend on the actual set of variables chosen, perhaps by introducing a set-dependent weighting factor, or perhaps by trimming. Such generalisations are explored in Sections 2.6-2.7. Brief bibliographic comments are in Section 2.8.
